By ESPNSTAR.com staff
Cole first made his name in English football at the Boleyn Ground from 1998 to 2003 before sealing his big-money move to Chelsea.
After a successful spell at Stamford Bridge, where he won eight major trophies including three Premier League titles, the England international became Roy Hodgson's marquee signing at Liverpool in 2010.
However, Cole failed to settle at Anfield and even spent last season on loan at Ligue 1 outfit Lille. Cole made a total of 42 appearances for Liverpool until the Reds decided to payoff the 31-year-old's contract to allow him to sign for the Hammers on a free transfer in the newly opened transfer window.
Cole has signed a 18 month contract with the Hammers and will wear his old No. 26 shirt.
"It is a great move for me," Cole said on the West Ham website.
"Coming back here brings back all the memories of the pitches I learnt how to play on. This is where I learnt my trade and I'm happy to have another chance to be here. I've always loved West Ham and I hope I can give the club a few memorable seasons.
"The timing was right for me to come back and I'm happy. I'm back in London and I'm delighted to be here. I want to be here and I want to make an impact."
Cole's last goal for Liverpool came in a 3-2 win over the Hammers at Upton Park in December. He praised West Ham boss Sam Allardyce for the job he has done so far.
"Sam didn't have to sell me the club for me to come back," Cole said.
"For me, I have had 18 months at Liverpool where I haven't played much football and Sam wants to play me. I'm going to need games to get back to my best, but I want to play football and come here and help the team to make an impact.
"I could see from the outside what a great bunch of lads we have here and there is a great spirit. I'm excited."
Cole underwent his West Ham medical on Thursday.